Classifications

• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N60/00—Superconducting devices
  • H10N60/10—Junction-based devices
  • H10N60/12—Josephson-effect devices
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
  • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10N60/00—Superconducting devices
  • H10N60/80—Constructional details
  • H10N60/805—Constructional details for Josephson-effect devices
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals

Definitions

• a quantum system that can be manipulated and measured tends to interact with uncontrolled degrees of freedom in its environment leading to decoherence. This presents a challenge to the experimental investigation of quantum effects and in particular to the field of quantum computing, where qubits must remain coherent while operations are performed. Most noisy environments are only locally correlated and thus cannot decohere quantum information encoded in a non-local manner.
• cQED circuit quantum electrodynamics
• the method comprises operating at least one energy source to drive a Kerr oscillator at a frequency wherein the Kerr oscillator comprises a plurality of superconducting nonlinear asymmetric inductive elements (SNAILs) coupled to one another in series, each of the plurality of SNAILs comprising a plurality of first Josephson junctions coupled in series and a second Josephson junction coupled in parallel with the plurality of first Josephson junctions, each of the plurality of SNAILS having a transition frequency and wherein [0006]
• ⁇ is an integer multiple of
• ⁇ is a Kerr nonlinearity of the plurality of SNAILs of the Kerr oscillator.
• the method further comprises operating the at least one energy source to drive a readout resonator at a frequency to thereby produce readout of a quantum state of the Kerr oscillator, wherein the readout resonator is coupled to the plurality of SNAILs of the Kerr oscillator and has a resonant frequency ⁇ ⁇ .
• a tunneling energy of the second Josephson junction is less than a tunneling energy of each of the first Josephson junctions.
• each of the plurality of SNAILs comprises a superconducting ring connected between two nodes.
• the superconducting ring comprises a first ring portion comprising the plurality of first Josephson junctions connected in series, wherein each second Josephson junction of the plurality of second Josephson junctions has the same tunneling energy and a second ring portion comprising the second Josephson junction in parallel with the plurality of first Josephson junctions between the two nodes.
• the method further comprises operating one or more magnetic flux generation devices to generate an external DC magnetic flux through the superconducting ring of each of the plurality of SNAILs.
• the external DC magnetic flux is between 0.25 ⁇ 0 and 0.50 ⁇ 0 , where ⁇ 0 is the magnetic flux quantum.
• the frequency is between 5 GHz and 8 GHz. [0013] In some embodiments, the frequency is between 5.5 GHz and 6.5 GHz. [0014] In some embodiments, is between 300 kHz and 400 kHz. [0015] In some embodiments, is between 310 kHz and 330 kHz. [0016] Some embodiments are directed to a circuit quantum electrodynamics (cQED) system.
• cQED circuit quantum electrodynamics
• the second Josephson junction is characterized by a superconducting phase difference, ⁇ , wherein the SNAIL has a potential that varies as a function of the superconducting phase difference, ⁇ , and has a single potential well, wherein the potential has a non-zero ⁇ 3 term and a ⁇ 4 term that is equal to zero.
• each of the plurality of SNAILs comprises two first Josephson junctions.
• the first Josephson junction is formed from two Dolan bridges.
• a tunneling energy of the second Josephson junction is less than a tunneling energy of each of the first Josephson junctions.
• the tunneling energy of each first Josephson junction is and the tunneling energy of each second Josephson junction is where is less than 0.50 and greater than 0.20.
• the external DC magnetic flux generated by the one or more magnetic flux devices is between 0.25 ⁇ 0 and 0.50 ⁇ 0 , where ⁇ 0 is the magnetic flux quantum.
• the Kerr oscillator is formed on a sapphire chip suspended within a cavity.
• the choice of the states of the bosonic system that represent the two states of the qubit may be referred to as the “codewords” for the selected code. While a selection of and as the codewords represents a perfectly valid code, it fails to be robust against many errors, such as boson loss. That is, when a boson loss occurs in the bosonic system, the state of the bosonic system prior to the boson loss may be unrecoverable with this code. [0045] In general, the choice of code affects how robust the system is to errors, such that the code used determines to what extent a prior bosonic state can be faithfully recovered when an error occurs.
• the present techniques relate to an oscillator design that has less bare nonlinearity than is conventionally thought to be necessary for efficient operation.
• the oscillator may be driven at a frequency that is detuned away from the frequency at which a nonlinear oscillator is typically driven.
• the detuned drive frequency may be substantially different from the typical drive frequency, and furthermore may be a frequency that may be expected to produce a low coherence time without also engineering the reduced nonlinearity described above.
• a quantum oscillator as described herein may be a Kerr nonlinear oscillator. This oscillator is characterized by having a small oscillation frequency which changes by a particular frequency – the Kerr frequency – when an excitation quantum is added to the system.
• an time-varying drive applied to the oscillator at a particular frequency may bifurcate the ground state of the oscillator into the cat states described above, thereby allowing the Kerr nonlinear oscillator to be operated as a qubit exhibiting the cat states (the resulting oscillator may be referred to herein as a “Kerr-cat qubit,” or simply a “Kerr-cat”).
• the techniques described herein realize specific drive frequencies at which a Kerr nonlinear oscillator (hereinafter, “Kerr oscillator”) may exhibit states with particularly long coherence times that are also resilient to strong drive amplitudes.
• an oscillating drive applied to a Kerr oscillator may have a frequency that is selected to be one of a set of particular detuning frequencies that have been determined by the inventors to produce an oscillator with a desirably long coherence time.
• a Kerr oscillator may be driven at a drive frequency, that is twice the transition frequency of the Kerr oscillator, Preferably, however, the Kerr oscillator may be driven at a frequency that is detuned from the frequency by particular multiples of a detuning parameter ⁇ .
• This drive frequency may be written herein as wherein , where is a positive or negative integer, and ⁇ is the Kerr nonlinearity of the Kerr oscillator.
• the squeezing drive may have a frequency that is detuned below twice the transition frequency of the Kerr oscillator (i.e., ⁇ 0).
• ⁇ twice the transition frequency of the Kerr oscillator
• the inventors have recognized that increasing the magnitude of ⁇ provides for a continuous reduction in the tunnelling amplitude between the cat states of the Kerr oscillator, and in addition increasing the magnitude of ⁇ specifically by multiples of 2 also provides for a discrete cancellation of tunnelling between the cat states.
• FIG. 1 is a block diagram of an illustrative quantum system suitable for practicing techniques described herein, according to some embodiments.
• the squeezing drive 115 may be provided with a frequency where is the transition frequency of the Kerr oscillator 110.
• the transition frequency, , of the Kerr oscillator 110 may be determined, for example, using two-tone spectroscopy. Two energy signals may be applied to the Kerr oscillator 110, including a probe tone with a frequency varied around an expected transition frequency of the Kerr oscillator 110 and a static tone used to monitor the Kerr oscillator 110. When the probe tone frequency approaches the transition frequency, the voltage response of the Kerr oscillator 110 is observed to decrease.
• a suitable value of may therefore be selected through the selected value of ⁇ .
• Desirable values of ⁇ are generalized as where Drive frequencies with these values of ⁇ produce multiple degenerate states of the Kerr oscillator.
• ⁇ 0, the ground state only is bifurcated, as described above.
• ⁇ is increased in magnitude while negative, additional resonances are produced, independent of the amplitude of the squeezing drive.
• the transferred photons may be emitted from the readout resonator and collected with a quantum-limited measurement apparatus to read the cat state of the Kerr oscillator. If the amplitude of the squeezing drive is sufficiently large, the emitted photons are replenished by the squeezing drive to maintain self- oscillation within the Kerr oscillator, thereby making the cat state measurement quantum non-demolition (QND).
• QND cat state measurement quantum non-demolition
• the resonant frequency of the readout resonator is displaced conditioned on the cat state of the Kerr oscillator that is populated, and thus serves as a cat quadrature readout (CQR) scheme.
• the Kerr oscillator may be implemented as a circuit quantum electrodynamics (cQED) system.
• system 100 may comprise a Kerr oscillator 110 comprising one or more nonlinear circuit elements, arranged with a resonant cavity (e.g., a microwave transmission line cavity), which is coupled to one or more ports for supplying one or more electromagnetic drives (e.g., microwave drives) 115 and 125 into the cavity to cause resonant behavior of the Kerr oscillator and readout resonator.
• a resonant cavity e.g., a microwave transmission line cavity
• the readout resonator may be implemented, for example, as a resonant structure mechanically supported within the cavity (e.g., a suspended resonator comprising a thin superconducting film coating a dielectric substrate), or as a stripline resonator.
• the Kerr oscillator may comprise a plurality of nonlinear components.
• the nonlinear elements may include any suitable nonlinear elements, including but not limited to superconducting nonlinear asymmetric inductive elements (SNAILs, described further below), superconducting quantum interference devices (SQUIDs), cold atoms controlled by an optical tweezer system, Josephson junctions, and/or any other suitable components.
• the plurality of nonlinear components may be coupled together in series. Coupling nonlinear component together in this manner may produce an oscillator with less bare nonlinearity than may be conventionally considered advantageous; however, as described above, the inventors have recognized that nonetheless such an oscillator has desirable properties when driven in a particular manner.
• the energy source 105 includes any source(s) of energy, including one or more sources of electromagnetic radiation, which may be arranged to direct the squeezing drive and/or readout drive to the Kerr oscillator 110. Each of these drives may be operated independently or simultaneously by the energy source.
• the energy source may comprise a laser or a microwave emitter.
• the energy source 105 may be coupled to the Kerr oscillator 110 via any suitable components, such as via one or more transmission lines (e.g., striplines and/or waveguides).
• the readout resonator 120 may be coupled to the Kerr oscillator 110 via any suitable coupling, including but not limited to electromagnetic coupling, piezoelectric coupling, and/or magnetostrictive coupling. In some cases the readout resonator and Kerr oscillator may be dispersively coupled.
• the energy source(s) 105 may be configured to apply one or more drives, in addition to the squeezing drive and the readout drive, to the Kerr oscillator to manipulate the state of the oscillator (e.g., to prepare a desired quantum state, to perform quantum gates on the state, etc.).
• the Kerr oscillator 110 when driven by squeezing drive 115, may exhibit a coherence time of equal to or greater than 1 millisecond, 5 milliseconds, 10 milliseconds, 20 milliseconds, 50 milliseconds, 100 milliseconds, 200 milliseconds, 500 milliseconds, 1000 milliseconds, or 1250 milliseconds.
• the Kerr oscillator 110 when driven by squeezing drive 115, may exhibit a coherence time of less than or equal to 1000 milliseconds, 500 milliseconds, 200 milliseconds, 100 milliseconds, 50 milliseconds, 20 milliseconds, or 10 milliseconds. Any suitable combinations of the above-referenced ranges are also possible (e.g., a coherence time of greater or equal to 500 milliseconds and less than or equal to 1000 milliseconds).
• the readout fidelity of the Kerr oscillator 110, when driven by squeezing drive 115 may also be greater than 99%. [0064] FIG.
• Ports 201 and 202 provide a mechanism for a coupled energy source (e.g., microwave emitter) to direct energy into the cavity at a desired amplitude and frequency (e.g., to input a squeezing drive 215 and/or a readout drive, not shown).
• a coupled energy source e.g., microwave emitter
• the package of system 200 may comprise a Purcell filter.
• the Purcell filter may be provided to protect the Kerr-cat qubit from spontaneous emission while maintaining a strong coupling to the cavity.
• the Purcell filter may comprise with two open-circuited transmission- line stubs.
• the transition frequency ⁇ ⁇ of the Kerr oscillator 220 may be greater than or equal to 5 GHz, 5.5 GHz, 5.8 GHz, 6.0 GHz, 6.1 GHz, 6.2 GHz, 6.3 GHz or 6.5 GHz. In some embodiments, the transition frequency of the Kerr oscillator 220 may be less than or equal to 7 GHz, 6.5 GHz, 6.4 GHz, 6.3 GHz, 6.2 GHz, 6.1 GHz, 6.0 GHz or 5.9 GHz. Any suitable combinations of the above-referenced ranges are also possible (e.g., a transition frequency of greater or equal to 6.0 GHz and less than or equal to 6.4 GHz, etc.).
• Kerr nonlinearity of a Kerr oscillator may be measured in various ways, including by supplying a probe tone to the Kerr oscillator while varying the frequency of the probe tone. When the probe tone excites the oscillator, the readout signal produced from the coupled readout resonator changes due to the coupling between the Kerr oscillator and readout resonator.
• the frequency of the squeezing drive 215 may be less than or equal to 14 GHz, 13 GHz, 12.8 GHz, 12.6 GHz, 12.4 GHz, 12.2 GHz, 12 GHz or 11.8 GHz. Any suitable combinations of the above-referenced ranges are also possible (e.g., a frequency of greater or equal to 12.4 GHz and less than or equal to 12.8 GHz, etc.).
• the frequency of the readout drive may be greater than or equal to 2 GHz, 2.1 GHz, 2.2 GHz, 2.3 GHz, 2.4 GHz, 2.5 GHz, 2.6 GHz or 2.7 GHz.
• FIG. 3A is a schematic diagram of a SNAIL 300, according to some embodiments.
• the SNAIL 300 includes a superconducting ring 301 with two nodes 311 and 312. There are two paths along two different portions of the superconducting ring 301 that connect the first node 311 and the second node 312. [0075]
• the first ring portion includes multiple Josephson junctions 305, 306 and 307 connected in series. In some embodiments, there are no other circuit elements between one Josephson junction and the next Josephson junction.
• a Josephson junction is a dipole circuit element (i.e., it has two nodes).
• a first node of a first Josephson junction 305 may be directly connected to the first node 311 of the SNAIL, which may lead to some other external circuit element (not shown), a second node of the first Josephson junction 305 may be directly connected to a first node of a second Josephson junction 306, and a second node of the second Josephson junction 306 may be directly connected to a first node of a third Josephson junction 307.
• a second node of the third Josephson junction 307 is directly connected to a second node 312 of the SNAIL, which may lead to some other external circuit element (not shown).
• FIG. 3A illustrates the first ring portion including three Josephson junctions, any suitable number of Josephson junctions greater than one may be used.
• Josephson junctions 305, 306 and 307 are formed to be identical in some manner.
• one or more of (including all of): the tunneling energies, the critical current, and the size of the Josephson junctions 305, 306 and 307 may be the same.
• the second ring portion of the SNAIL 300 includes a single Josephson junction 308. In some embodiments, there are no other circuit elements in the second ring portion.
• a first node of a single Josephson junction 308 may be directly connected to the first node 311 of the SNAIL, which may lead to some other external circuit element (not shown), and a second node of the single Josephson junction 308 may be directly connected to the second node 312 of the SNAIL, which may lead to some other external circuit element (not shown).
• the single Josephson junction 308 has a smaller tunneling energy than each of Josephson junctions 305, 306 and 307. For this reason, the single Josephson junction 308 may be referred to as a “small” Josephson junction and Josephson junctions 305, 306 and 307 may be referred to as “large” Josephson junctions.
• FIG. 3B illustrates the circuit element symbol for the SNAIL 300.
• the parameters that characterize the SNAIL 300 are the Josephson energy and the superconducting phase difference, ⁇ , of the small Josephson junction 308.
• the SNAIL 300 may controlled at least in part by threading a DC magnetic flux ⁇ ext through the superconducting ring 301.
• a magnetic flux generation device (not shown) may be positioned in proximity to the superconducting ring.
• an electrical coil may be formed in proximity to the ring 301.
• the coil may be next to the ring 301 and in the same plane as ring 301.
• a coil may be under the ring 301 in a different layer of the device 300.
• any number of large Josephson junctions may be used in the SNAIL 300.
• the above equation indicates that the potential is a function of a single degree of freedom ( ⁇ ) . This is because dynamics due to any intra-array modes are eliminated and only common excitations across the array of n Josephson junctions are considered. This reduction is valid when for each junction, where is the Coulomb charging energy of the junction with capacitance and when where is the capacitance to ground of each island between junctions.
• the parameters may be selected such that the SNAIL 300 has properties desirable for its application. For example, for ⁇ 0.8 and the SNAIL 300 will have a double-well potential, which is undesirable due to the resulting hysteresis affects. But the parameters can be adjusts to create a potential with a single minimum. Moreover, the potential may simultaneously be tuned to cancel the fourth-order (Kerr) term while keeping a substantial cubic term.
• Kerr fourth-order
• the potential may be Taylor expanded about its minimum value to obtain the effective potential for where are numerically determinable coefficients whose specific values depend on (which is three in the illustrated embodiments), [0084]
• the magnetic flux ⁇ threaded through the SNAILs 221 and 222 may be, in some embodiments, greater than or equal to 0.25 ⁇ 0 , 0.3 ⁇ 0 , 0.35 ⁇ 0 , 0.4 ⁇ 0 , 0.45 ⁇ 0 or 0.5 ⁇ 0 .
• the magnetic flux ⁇ threaded through the SNAILs 221 and 222 may be less than or equal to 0.5 ⁇ 0 , 0.45 ⁇ 0 , 0.4 ⁇ 0 , 0.35 ⁇ 0 , 0.3 ⁇ 0 or 0.25 ⁇ 0 . Any suitable combinations of the above-referenced ranges are also possible (e.g., a magnetic flux ⁇ of greater or equal to 0.3 ⁇ 0 and less than or equal to 0.35 ⁇ 0 , etc.).
• driving a Kerr oscillator with a squeezing drive having a frequency produces 1 degenerate states of the Kerr oscillator.
• 4A-4B may, when implemented as a cQED system such as that shown in FIGs.2A-2C, exhibit a coherence lifetime on the order of hundreds of microseconds.
• a loss of coherence may be observed when the squeezing drive frequency is adjusted away from due to tunnelling between the cat states. This tunnelling may be suppressed to some degree with a sufficiently strong squeezing drive amplitude (e.g., 3).
• a sufficiently strong squeezing drive amplitude e.g. 3
• FIGs. 5A-5B illustrate quantum spectra of a Kerr nonlinear oscillator as a function of the detuning ⁇ , according to some embodiments.
• the energy of various states of the Kerr oscillator are depicted as a function of The difference between FIGs.5A and 5B is in the value of wherein 0.5 in the case of FIG.5A, and 1.8 in the case of FIG.5B.
• a Kerr oscillator driven by a squeezing drive with a frequency slightly deviating from reaches a high transition probability within a microsecond (e.g., see the dark bands around at times of less than 1
• a Kerr oscillator driven by a squeezing drive with a frequency of retains a low transition probability for much longer time periods, especially at higher drive amplitudes.
• aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.
• the invention may be embodied as a method, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.
• some actions are described as taken by a “user.” It should be appreciated that a “user” need not be a single individual, and that in some embodiments, actions attributable to a “user” may be performed by a team of individuals and/or an individual in combination with computer-assisted tools or other mechanisms.
• the terms “approximately” and “about” may include the target value.
• the term “substantially equal” may be used to refer to values that are within ⁇ 5% of one another in some embodiments, within ⁇ 2% of one another in some embodiments, within ⁇ 1% of one another in some embodiments, and yet within ⁇ 0.5% of one another in some embodiments. [00101]
• the term “substantially” may be used to refer to values that are within ⁇ 5% of a comparative measure in some embodiments, within ⁇ 2% in some embodiments, within ⁇ 1% in some embodiments, and yet within ⁇ 0.5% in some embodiments.

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